[ecco-support] Change-of-variable formulas for adjoint sensitivities

[Matthew Mazloff]

Hi Christopher

Ariane V, Bruce C, and I worked this out some time ago (~2013), so the details are blurry. But I am fairly certain that it works out fine to just take the curl of the sensitivity of J to the wind stress. That should give you the sensitivity to the curl. The operation is linear - we should be able to work this out.... Happy to discuss, though like I said, last time I thought about this was ~2013.

Matt
 

> On Jul 6, 2020, at 3:20 PM, Christopher Wolfe <christopher.wolfe at stonybrook.edu> wrote:
> 
> Hi all:
> 
> Does any know of a simple formula (or reference) for a changing the dependent variables of adjoint sensitivities? For example, suppose you have the sensitivities of a cost function, J, to zonal and meridional wind stress. Is there a straightforward way to use these to calculate the sensitivity of J to the wind stress curl? I figured that there ought to be, but I got buried under a mountain of functional analysis and worried I was overthinking it.
> 
> Not sure if this is the right forum. If not, I’m happy to ask the wider MITgcm-support list.
> 
> Thanks in advance for any pointers!
> 
> Cheers,
> Christopher
> 
> 
> ----------------------------------------------------------------------------
> Christopher L. Pitt Wolfe
> Associate Professor (Physical Oceanography)
> School of Marine and Atmospheric Sciences
> Stony Brook University
> christopher.wolfe at stonybrook.edu <mailto:christopher.wolfe at stonybrook.edu>             631-632-3152
> ----------------------------------------------------------------------------
> 
> 
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